(a) No vehicle shall be, or continue to be, registered in the name of any person required to file proof of financial responsibility for the future unless proof is furnished for the vehicle.
(b) Proof of financial responsibility when required under this chapter, with respect to the vehicle or with respect to a person who is not the owner of the vehicle, may be given by filing:
(1) A certificate of insurance as provided in § 27-19-712; or
(2) A certificate of self-insurance, as provided in § 27-19-107, supplemented by an agreement by the self-insurer that, with respect to accidents occurring while the certificate is in force, he or she will pay the same amounts that an insurer would have been obliged to pay under an owner's motor vehicle liability policy if it had issued such a policy to the self-insurer.